Mexican president Felipe Caldéron is accused of war crimes in the counry's battle against drug gangs. Photograph: Alfredo Estrella/AFP/Getty Images

Mexican human rights activists have asked the international criminal court to investigate President Felipe Caldéron, as well as top officials and the country's most-wanted drug trafficker, accusing them of allowing subordinates to kill, torture and kidnap civilians.

Netzai Sandoval, a Mexican human rights lawyer, filed a complaint with the ICC in The Hague on Friday, requesting an investigation of the deaths of hundreds of civilians at the hands of the military and traffickers.

More than 45,000 people have died in drug-related violence in Mexico since 2006 as powerful cartels fight security forces and each other for control of smuggling routes into the neighbouring United States and other countries.

"The violence in Mexico is bigger than the violence in Afghanistan, the violence in Mexico is bigger than in Colombia," Sandoval said.

"We want the prosecutor to tell us if war crimes and crimes against humanity have been committed in Mexico, and if the president and other top officials are responsible."

Signed by 23,000 Mexican citizens, the complaint names the Sinaloa cartel boss Joaquin "Shorty" Guzman, who has a $5m bounty on his head, as well as the public security minister, Genaro Garcia Luna, and the commanders of the army and navy.

A decision by ICC prosecutors on whether to investigate could take months or years, legal experts said.

The Mexican government has denied it is "at war" and said the use of the military in its battle against drug gangs is a temporary measure taken at the request of state governments. "The established security policy in no way constitutes an international crime. On the contrary, all its actions are focused on stopping criminal organisations and protecting all citizens," said an interior ministry statement.

The office of the ICC prosecutor said in a statement it had the request, which it would study and "make a decision in due course".

Richard Dicker, an international justice expert with Human Rights Watch, said: "There are a large number of boxes that the prosecutor would need to check off before he could actually open an investigation.

"It's possible ... but I think you want to be clear on what the challenges and obstacles are."

In considering the case, ICC chief prosecutor Luis Moreno Ocampo will have to decide if the crimes presented in the activists' complaint, such as the torture of criminal suspects, qualify as crimes against humanity. "The crimes would have to be widespread or systematic, carried out by a state or organisation in attacks on a civilian population," Dicker said.

"It's certainly very arguable," said William Schabas, professor of international law at Middlesex University. "The prosecutor has been very focused on Africa. The pattern is he stays within the comfort zone of the United States. Going after Mexicans for the war on drugs falls outside that comfort zone."

Activists say Caldéron has systematically allowed Mexican troops to commit abuses against civilians since the military was deployed to fight drug traffickers in 2006. More than 50,000 soldiers are battling cartels around the country, while the ranks of federal police have swelled from 6,000 to 35,000 under Caldéron's watch.

A Human Rights Watch report said there was evidence Mexican police and soldiers were involved in 170 cases of torture, 24 murders and 39 forced disappearances in five Mexican states. "We have known for five years that the Mexican army is committing sexual abuse, executing people, torturing people and kidnapping, and there have been no sanctions," Sandoval said.

Mexico's national human rights commission received more than 4,000 complaints of abuses by the army from 2006 to 2010. In the same period it issued detailed reports on 65 cases involving army abuse, according to Human Rights Watch.

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